Isogeometric robust topology optimization method for thermomechanically coupled composite structures

Abstract

The application discloses a method for isogeometric robust topology optimization of a composite material structure considering thermal coupling, and establishes an isogeometric robust topology optimization model of the composite material structure considering thermal coupling, describes the temperature inside the structure as an uncertainty variable satisfying a non-accurate probability distribution, solves the corresponding worst target robust performance value through a gradient search algorithm and Gauss-Hermite integration, and proposes a constraint performance reliability analysis method considering fluctuation of the worst limit state, solves the sensitivity of the worst target performance function, the worst limit state function and the volume constraint function, and obtains the optimal topology structure through a moving asymptote method. The robust topology optimization model of the composite material structure established by the application can reflect the temperature fluctuation inside the structure under actual working conditions, can efficiently obtain an optimization result, and has good engineering application value.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of structure optimization, and particularly relates to an equal geometric robust topology optimization method for composite material structures considering thermal coupling. BACKGROUND

[0002] In the fields of rail transit, aerospace, etc., the cutter head of a shield tunneling machine, the landing gear of an airplane, etc., when working, the temperature inside the structure is often higher than the reference ambient temperature due to the severe friction between parts, and the key structure needs to withstand external load and structural strain caused by material thermal expansion, so the topology optimization of such structures needs to consider the thermal expansion phenomenon of the material.

[0003] Existing uncertainty topology optimization considering thermal coupling mainly focuses on material properties, external load, etc. Uncertainty factors are studied, and less consideration is given to the fluctuation of the internal temperature of the structure. However, in actual working conditions, the internal temperature of complex components is usually affected by uncertainty factors such as working state and lubrication level, and the change in the internal temperature of the structure will have a more obvious impact on the optimization results of structures with high thermal expansion coefficients, so there is an urgent need for a composite material structure topology optimization method considering the fluctuation of the internal temperature of the structure to meet the actual engineering needs. SUMMARY

[0004] To solve the problems of the prior art and achieve the purpose of designing a structure with good stiffness and strength in a high-temperature scene, the present application adopts the following technical solutions:

[0005] The equal geometric robust topology optimization method for composite material structures considering thermal coupling comprises the following steps:

[0006] Step 1: An equal geometric analysis model of the composite material structure is constructed to obtain the density of the control points;

[0007] Step 2: Based on the internal temperature uncertainty description of the composite material structure, the overall thermal load considering the fluctuation of the internal temperature is constructed according to the uncertainty description and the density of the control points, and the overall flexibility of the composite material structure is generated; the density of the control points is taken as a design variable, and the equal geometric robust topology optimization model of the composite material structure considering thermal coupling is constructed by combining the uncertainty description, the overall flexibility, the stress constraint and the utilization rate constraint of the optimization space, so as to minimize the mean value and the standard deviation of the thermal flexibility of the composite material structure under the influence of the internal temperature uncertainty;

[0008] Step 3: The overall stiffness matrix of the composite material structure considering the bimodulus characteristics is calculated;

[0009] Step 4: Calculate the thermal strain of the composite structure at the Gauss point, combine the elastic tensor matrix considering the bimodulus characteristics, solve the overall thermal load of the composite structure considering internal temperature fluctuations, and solve the overall displacement under the influence of internal temperature uncertainty by the overall thermal load and the overall stiffness matrix of the structure, which is used to determine the overall flexibility; solve the global failure coefficient of the composite structure considering internal temperature fluctuations, which is used for stress constraints;

[0010] Step 5: Construct the objective function based on the mean and standard deviation of the thermal flexibility of the composite structure and solve it to get the worst target performance function;

[0011] Step 6: Calculate the worst limit state corresponding to the stress constraint;

[0012] Step 7: Update the control point density according to the worst target performance function, the worst limit state, and the density sensitivity of the optimization space utilization constraint with respect to the control point, to get the optimal design variable.

[0013] Further, the step S2 comprises the following steps:

[0014] Step 2.1: Describe the internal temperature of the composite structure affected by multi-source uncertainty as a probability variable satisfying the non-accurate normal distribution T I represents the internal temperature variable of the composite structure, I μ and I σ represent the mean and standard deviation of the internal temperature variable of the composite structure with interval characteristics, specifically:

[0015]

[0016] wherein, and represent the upper and lower limit values of the mean and standard deviation of the internal temperature variable of the composite structure;

[0017] Step 2.2: By considering the thermal expansion phenomenon of the composite material under high temperature scenarios, construct the overall thermal load F th (ρ,T I ), ρ represents the control point density vector;

[0018] Step 2.3: Based on the non-accurate probability variable and the overall thermal load, construct the isogeometric robust topology optimization model of the composite structure considering thermal-mechanical coupling:

[0019]

[0020] wherein, ρ i,j represents the density of the control point P i,j , and respectively represent the mean and standard deviation of the thermal compliance of the composite structure considering the influence of internal temperature uncertainty, c(ρ, T I ) represents the thermal compliance of the composite structure under the influence of internal temperature uncertainty, u e (ρ, T I ) represents the displacement vector of element e under the influence of internal temperature uncertainty of the composite structure, which is abbreviated as below, N e represents the stiffness matrix of element e considering the bimodulus property, g V (ρ) represents the optimization space utilization constraint function, V(ρ) represents the current optimization space size, V0 and [V] respectively represent the design domain size and the upper limit value of the space utilization constraint, P(·) represents the probability calculation function, and [ω TW ] respectively represent the global failure coefficient constraint performance function of the composite structure constructed based on the Tsai-Wu failure criterion and the set global failure coefficient upper limit value, P t represents the pre-set stress constraint reliability requirement, K B (ρ) represents the overall stiffness matrix of the composite structure considering the bimodulus property, U represents the overall displacement amplitude vector of the composite structure, F m represents the external load on the composite structure.

[0021] Further, the step 3 comprises the following steps:

[0022] Step 3.1: Obtain the elastic tensor matrix considering the bimodulus property based on the Patel model Solve the element stiffness matrix of the composite structure considering the bimodulus property

[0023] Step 3.2: Calculate the overall stiffness matrix K B (ρ) of the composite structure through the element stiffness matrix .

[0024] Further, the isogeometric analysis model in the step 1 is a non-uniform rational B-spline grid model, the overall grid model is Gauss subdivided, and the density of the i-th row, j-th column element Gauss point in the e-th element is obtained from the corresponding control point of the element e

[0025] Further, the step 4 comprises the following steps:

[0026] Step 4.1: Calculate the thermal strain of the composite structure at the element Gauss point , specifically:

[0027]

[0028] in, Φ represents the structural thermal strain vector at the Gaussian point of the element. c T represents the vector of thermal expansion coefficients of composite materials. R Indicates the reference ambient temperature; T I Indicates the internal temperature variable of a composite material structure;

[0029] Using the Gaussian subdivision method, the thermal load corresponding to the e-th element is calculated as follows:

[0030]

[0031] in, N represents the thermal load vector at element e. G This represents the number of discrete Gaussian integration points in the row and column directions within each element of the parameter domain. This represents the weights corresponding to the discrete Gaussian integral points in the row and column directions within each element of the parameter domain. Represents the Gaussian point of the unit The strain displacement matrix at J e Let denote the Jacobian matrix of element e, and det(·) denotes the operation of solving the determinant. This represents the elastic tensor matrix considering the dual-modulus property.

[0032] Step 4.2: By combining the thermal load vector at calculation unit e, the overall thermal load F of the composite material structure is obtained. th (ρ,T I );

[0033] Step 4.3: Solve for the Gaussian point of the composite material structural element considering internal temperature fluctuations. The stress vector is as follows:

[0034]

[0035] in, This represents the stress vector at a Gaussian point in an element that takes into account internal temperature fluctuations; it is abbreviated below as follows.

[0036] Step 4.4: Calculate the global failure coefficient of the composite material structure based on the Tsai-Wu failure criterion and the P-mean condensation function. Specifically:

[0037]

[0038] Where, N e Indicates the number of equal geometric units. represents the failure coefficient at the element Gauss point obtained by Tsai-Wu failure criterion and the element Gauss point stress vector represents the failure coefficient at the element Gauss point obtained by Tsai-Wu failure criterion and the element Gauss point stress vector t represents the P-mean aggregation function coefficient of the stress constraint function.

[0039] Further, the step 5 comprises the following steps:

[0040] Step 5.1: Introducing weight coefficient w T , define the weighted objective function

[0041]

[0042] wherein, and respectively represent the mean value and standard deviation of the thermal compliance of the composite structure considering the influence of internal temperature uncertainty, c(ρ, T I ) represents the thermal compliance of the composite structure under the influence of internal temperature uncertainty, ρ represents the density of the control point, T I represents the internal temperature variable of the composite structure;

[0043] Step 5.2: Calculate the approximation of the origin matrix E[c I (ρ, T m )] of the thermal compliance c(ρ, T I ) of the composite structure, and calculate the mean value and standard deviation of the thermal compliance of the structure under the influence of the internal temperature uncertainty T I ;

[0044] Step 5.3: Rewrite the objective function as:

[0045]

[0046] wherein, represents the hth Gauss-Hermite integral point corresponding to the internal temperature value of the structure; represents the thermal compliance of the structure under the hth Gauss-Hermite integral point corresponding to the internal temperature ;

[0047] Step 5.4: Considering the interval characteristics of the internal temperature variable distribution parameters, solve the objective function about the sensitivity of the mean value I μ and the standard deviation I σ of the internal temperature of the structure, and obtain the internal temperature distribution parameter value and worst temperature condition and worst target performance function

[0048] Further, the step 5.2 specifically comprises the following steps:

[0049] Step 5.2.1: considering the probability distribution characteristics of the internal temperature variable, the internal temperature variable T I of the structure is converted into a standard normal variable T s by standardization, specifically as follows:

[0050]

[0051] Step 5.2.2: based on Gauss-Hermite integral calculation, the origin moment approximation values when m = 1, 2 are calculated, specifically as follows:

[0052]

[0053] wherein c(ρ, T I ) and c s (ρ, T s ) represent the structural thermal compliances represented by the internal temperature variable T I of the structure and the standard normal variable T s , respectively, ρ represents the density of the control point, φ(T s ) represents the probability density distribution function of the standard normal variable T s , H represents the number of selected Gauss-Hermite integral points, w h (h = 1, 2, …, H) represents the weight corresponding to the hth Gauss-Hermite integral point; T s h is the standard normal variable value corresponding to the hth Gauss-Hermite integral point, c s (ρ, T s h ) represents the structural thermal compliance represented by T s h ;

[0054] Step 5.2.3: the mean value and standard deviation of the structural thermal compliance under the influence of the internal temperature uncertainty T I of the structure are calculated, specifically as follows:

[0055]

[0056] Further, the step 6 comprises the following steps:

[0057] Step 6.1: based on the stress constraint performance function , a limit state function is constructed, represented as:

[0058]

[0059] wherein, and [ω TW ] represent the global failure coefficient constraint performance function of the composite structure constructed based on Tsai-Wu failure criterion and the set upper limit value of the global failure coefficient, respectively, ρ represents the density of the control point, T I represents the internal temperature variable of the composite structure;

[0060] Step 6.2: considering the internal temperature variable T I of the structure in the original space, the variable T I is transformed into the standard normal space through standardization processing, and the limit state function is rewritten as the form represented by the standard normal variable T s , the interval variable I s and the interval variable I μ . σ

[0061] Step 6.3: establishing a reliability model for solving the worst limit state function on the reliability index surface under the influence of non-accurate probability variables:

[0062]

[0063] wherein, β t represents the reliability index corresponding to the constraint performance function, and is calculated according to the corresponding reliability requirement P t ; β t = Φ -1 (P t ); Φ -1 (·) represents the inverse function of the standard normal cumulative distribution function, ||·|| represents the solving modulus operation, μ T represents the mean value of the internal temperature variable of the structure, σ T represents the standard deviation of the internal temperature variable of the structure, and represent the upper and lower limit values corresponding to the upper and lower limit values of the mean value and the standard deviation of the internal temperature variable of the composite structure, respectively;

[0064] Step 6.4: calculating the stress limit state function about the sensitivity of the variable T s , I μ and I σ ; through the gradient search algorithm, the worst constraint performance point T s MPTP and the worst limit temperature mean value and the standard deviation are calculated.​ and combining to obtain the worst limit temperature T I MPTP and the worst limit state function

[0065] Further, in the step 7, the worst target performance function, the worst limit state function and the sensitivity of the optimization space utilization rate constraint with respect to the density of each unit control point are calculated; according to the calculation result of the control point density sensitivity, the control point density is updated in combination with the moving asymptote method, and the convergence condition is checked, that is, the average of the relative change degree of the worst target performance function in consecutive iterations is not higher than a threshold value, and if the convergence condition is not met, the iteration returns to step 3.

[0066] The equal geometry robust topology optimization system of the composite material structure considering thermal force coupling is used to perform topology optimization according to the equal geometry robust topology optimization method of the composite material structure considering thermal force coupling to obtain an optimal complex material structure design variable.

[0067] The advantages and beneficial effects of the present application are as follows:

[0068] Compared with the composite material structure topology optimization method without considering thermal force coupling and bimodulus characteristics, the present application fully considers the influence of material thermal expansion and bimodulus characteristics, and the obtained optimized structure is more in line with actual engineering requirements and has good stiffness and strength in a high temperature scene; the present application describes the internal temperature of the structure affected by multiple source uncertainty factors as a random variable satisfying an imprecise normal distribution, and proposes a target performance statistical moment solving method based on Gaussian-type quadrature and gradient search, uses Guass-Hermite integral to solve the approximate value of the target performance statistical moment, and uses the gradient search algorithm to determine the worst target performance function value, which can efficiently and accurately evaluate the target performance statistical value under the influence of imprecise probability variables; the present application proposes a structure constraint performance reliability analysis method considering the fluctuation of the worst limit state, simultaneously considers the probability distribution characteristics of the internal temperature variable of the structure and the interval characteristics of the distribution parameters, constructs a reliability analysis model considering the influence of imprecise probability variables, obtains the worst limit state function, and compared with the existing reliability evaluation method containing imprecise probability variables, can obtain a more optimal structure target performance. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 is a method flowchart of an embodiment of the present application.

[0070] Figure 2 is an initial design schematic diagram of a cutter disc support plate in an embodiment of the present application.

[0071] Figure 3 is an optimal topology diagram of a cutter disc support plate in an embodiment of the present application. DETAILED DESCRIPTION

[0072] The specific embodiments of the present application are described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely intended to illustrate and explain the present application, and are not intended to limit the present application.

[0073] As shown in Figure 1 , the present application proposes a method for isogeometric robust topology optimization of composite structures considering thermal coupling. By considering the material thermal expansion phenomenon of composite structures under high temperature scenarios and the temperature fluctuations inside the structure, the internal temperature of the structure which is susceptible to multiple source uncertainty factors such as lubrication level and operating state is described as a non-accurate probability variable. At the same time, the mean and standard deviation of the structural thermal flexibility are taken as the objective function, and the isogeometric robust topology optimization model of the composite structure under stress constraint and material consumption constraint is established, which fully reflects the high stiffness, high strength and lightweight design requirements of the composite structure under high temperature scenarios. At the same time, a target performance statistical moment solving method based on Gaussian-type quadrature and gradient search and a reliability analysis method considering the worst limit state fluctuation are proposed, which are used to efficiently solve the worst target performance function and the worst limit state function under the influence of non-accurate probability variables. On this basis, the sensitivity of the worst target performance function, the worst limit state function and the volume constraint function is derived and solved, and the optimal topology design scheme is obtained by using the moving asymptote method.

[0074] Step 1: Construct the isogeometric analysis model of the composite structure based on Non-Uniform Rational B-Splines (NURBS), and perform Gaussian subdivision on the NURBS grid model as a whole. The density of the i-th element in the ii-th row and jj-th column of the element e is obtained from the corresponding control point of the element e

[0075] In the embodiments of the present application, the actual application in the topology optimization design of a certain type of shield machine cutter disc support plate made of TM800s / M21 carbon fiber reinforced composite material is carried out, as shown in Figure 2 the cutter disc support plate design domain, the left end and the lower end of the cutter disc support plate are fixed, and the right end is subjected to a uniformly distributed load F acting horizontally to the left. The total load is 900N, and the equivalent uniformly distributed line load is 1.9912N / mm.

[0076] On the basis of constructing the NURBS curve, two direction node vectors u=(u0, u1,..., u 51+2+1 ) and v=(v0, v1,..., v 26+2+1 ) are introduced, 51*26 control points P i,j ,i=1,2,...,51;j=1,2,...,26 and 51*26 weights w​i,j i = 1, 2, …, 51; j = 1, 2, …, 26.

[0077] Step 2: Constructing an isogeometric robust topology optimization model of the composite structure considering thermal coupling, specifically comprising the following steps:

[0078] Step 2.1: Considering the internal temperature of the composite structure affected by multi-source uncertainty, describing it as a probability variable satisfying an inexact normal distribution Where T I represents the internal temperature variable of the composite structure, I μ and I σ represent the mean and standard deviation of the internal temperature variable of the composite structure with interval characteristics, specifically:

[0079]

[0080] Where, and represent the upper and lower limit values of the mean and standard deviation of the internal temperature variable of the composite structure.

[0081] In the embodiment of the present application, the cutter disc support plate as the composite structure, the mean and standard deviation of the internal temperature variable of the cutter disc support plate are as follows:

[0082]

[0083] Step 2.2: Considering the thermal expansion phenomenon of the composite material under high temperature scenarios, constructing the overall thermal load F th (ρ, T I ), ρ represents the control point density vector.

[0084] Step 2.3: Based on the inexact probability variable and the overall thermal load, constructing an isogeometric robust topology optimization model of the composite structure considering thermal coupling:

[0085]

[0086] Where ρ i,j represents the density of the control point P i,j , and represent the mean and standard deviation of the thermal compliance of the composite material structure considering the influence of the internal temperature uncertainty of the composite material structure, c(ρ, T I ) represents the thermal compliance of the composite material structure under the influence of the internal temperature uncertainty of the composite material structure, u e (ρ, T I) represents the displacement vector of unit e under the influence of the temperature uncertainty inside the composite structure, which is abbreviated as represents the stiffness matrix of unit e considering the bimodulus property, N e represents the number of units, g V represents the optimization space utilization constraint function, V(ρ) represents the current optimization space size, V0 and [V] represent the design domain size and the upper limit value of the space utilization constraint respectively, P(·) represents a probability calculation function, and [ω TW ] respectively represent the global failure coefficient constraint performance function of the composite structure constructed based on the Tsai-Wu failure criterion and the set upper limit value of the global failure coefficient, P t represents the pre-set stress constraint reliability requirement, K B (ρ) represents the overall stiffness matrix of the composite structure considering the bimodulus property, U represents the overall displacement amplitude vector of the composite structure, F m represents the external load borne by the composite structure.

[0087] Step 3: Constructing the overall stiffness matrix of the composite structure considering the bimodulus property, specifically including the following steps:

[0088] Step 3.1: Obtaining the elastic tensor matrix considering the bimodulus property based on the Patel model Solving the unit stiffness matrix of the composite structure considering the bimodulus property

[0089] Step 3.2: Calculating the overall stiffness matrix K B (ρ) of the composite structure.

[0090] Step 4: Solving the thermal load and global failure coefficient of the composite structure considering the internal temperature fluctuation of the structure, specifically including the following steps:

[0091] Step 4.1: Calculating the thermal strain of the composite structure at the unit Gauss point , specifically:

[0092]

[0093] wherein, represents the thermal strain vector of the structure at the unit Gauss point, Φ c represents the thermal expansion coefficient vector of the composite material, T R represents the reference environmental temperature;

[0094] In the embodiment of the application, the thermal strain vector at the unit Gauss point is:

[0095]

[0096] Using the Gaussian subdivision method, the thermal load corresponding to the e-th element is calculated as follows:

[0097]

[0098] in, N represents the thermal load vector at element e. G This represents the number of discrete Gaussian integration points in the row and column directions within each element of the parameter domain. This represents the weights corresponding to the discrete Gaussian integral points in the row and column directions within each element of the parameter domain. Represents the Gaussian point of the unit The strain displacement matrix at J e Let $e$ represent the Jacobian matrix of element $e$, and $det(·)$ denotes the operation of solving the determinant.

[0099] Step 4.2: By combining the thermal load vector at calculation unit e, the overall thermal load F of the composite material structure is obtained. th (ρ,T I );

[0100] Step 4.3: Solve for the Gaussian point of the composite structural element considering internal temperature fluctuations. The stress vector is as follows:

[0101]

[0102] in, This represents the stress vector at a Gaussian point within the element, taking into account internal temperature fluctuations within the structure. It is abbreviated below as...

[0103] Step 4.4: Calculate the global failure coefficient of the composite material structure based on the Tsai-Wu failure criterion and the P-mean condensation function. Specifically:

[0104]

[0105] Where, N e Indicates the number of equal geometric units. This represents the failure criterion derived from the Tsai-Wu failure criterion and the stress vector at the Gaussian point of the element. The failure coefficient at the Gaussian point of the element is obtained, p t The P-mean condensation function coefficients represent the stress constraint function;

[0106] In this embodiment of the invention, the failure coefficient at the Gaussian point of the element is:

[0107]

[0108] Step 5: Calculate the mean and standard deviation of the thermal flexibility of the composite material structure based on Gaussian quadrature and gradient search, specifically:

[0109] Step 5.1: Introduce weighting coefficient w T Define the weighted objective function

[0110]

[0111] Step 5.2: Calculate the thermal flexibility c(ρ,T) of the composite material structure. I Origin Moment E[c m (ρ,T I The approximate value of )] is as follows:

[0112] Step 5.2.1: Considering the probability distribution characteristics of the internal temperature variable of the structure, the internal temperature variable T is standardized. I Convert to standard normal variable T s Specifically:

[0113]

[0114] Step 5.2.2: Calculate the approximate value of the origin moment when m = 1, 2 based on the Gauss-Hermite integral, specifically as follows:

[0115]

[0116] Where, c(ρ,T) I ) and c s (ρ,T s ) represent the temperature variables T inside the structure, respectively. I and standard normal variable T s The structural thermal flexibility is represented by φ(T). s ) represents the standard normal variable T s The probability density distribution function; H represents the number of Gauss-Hermite integration points selected; w h (h = 1, 2, ..., H) represents the weight corresponding to the h-th Gauss-Hermite integration point; Tsh is the standard normal variable value corresponding to the h-th Gauss-Hermite integration point, c s (ρ,T s h ) indicates that T s h The thermal flexibility of the structure is indicated;

[0117] Step 5.2.3: Calculate the internal temperature uncertainty T of the structure I The mean and standard deviation of the structural thermal flexibility under the influence are as follows:

[0118]

[0119] Step 5.3: rewrite the objective function as:

[0120]

[0121] where T I h represents the hth Gauss-Hermite integration point T s h corresponding to the internal temperature value of the structure; c(ρ, T I h ) represents the hth Gauss-Hermite integration point T s h corresponding to the internal temperature T I h of the structure under the structure thermal compliance;

[0122] Step 5.4: considering the interval characteristics of the internal temperature variable distribution parameters of the structure, solve the objective function about the sensitivity of the mean I μ and the standard deviation I σ of the internal temperature of the structure, and obtain the internal temperature distribution parameter value corresponding to the worst objective function value based on the gradient search algorithm and the worst temperature working condition and the worst objective performance function

[0123] In the embodiment of the present application, w h (h=1, 2, …, 5), correspondingly:

[0124]

[0125]

[0126] Step 6: solve the worst limit state function corresponding to the probability constraint function by the gradient search algorithm, specifically:

[0127] Step 6.1: construct the limit state function based on the stress constraint performance function , which is expressed as:

[0128]

[0129] In the embodiment of the present application, [ω TW ]=0.6, therefore, correspondingly:

[0130]

[0131] Step 6.2: Consider the internal temperature variable T in the original space I Satisfy the non-precise normal distribution, the variable T in the original space I Transformed into a standard normal space variable T by standardization s Rewrite the limit state function as a standard normal variable T s And interval variable I μ And I σ The form represented by

[0132] Step 6.3: Establish a reliability model for solving the worst limit state function on the reliability index surface under the influence of non-precise probability variables:

[0133]

[0134] Where β t Indicates the reliability index corresponding to the constraint performance function, and its corresponding reliability requirement P t Is calculated, β t = Φ -1 (P t ) ; Φ -1 (·) represents the inverse function of the standard normal cumulative distribution function, ||·|| represents the solution module operation, μ T Indicates the mean of the internal temperature variable of the structure, σ T Indicates the standard deviation of the internal temperature variable of the structure;

[0135] Step 6.4: Calculate the stress limit state function About the variable T s , I μ And I σ Sensitivity; Through the gradient search algorithm, the worst constraint performance point T on the reliability index surface is calculated s MPTP And the worst limit temperature mean And standard deviation And combined to get the worst limit temperature T I MPTP And the worst limit state function

[0136] Step 7: Solve the worst target performance function The worst limit state function And the volume constraint function g V (ρ) about each unit control point density ρ i,jsensitivity of the worst target performance function, the worst limit state function and the volume constraint function, the control point density is updated by using the moving asymptote method; a convergence condition (the average of the relative change degree of the worst target performance function and the worst limit state function in the last three iteration steps is not higher than a threshold value 0.03) is checked; if the convergence condition is not met, the step 3 iteration is returned.

[0137] In the embodiment of the present application, as shown in the figure Figure 3 is an optimal topology diagram of the cutter support plate, the convergence condition is met at 25 iterations, and the average of the thermal flexibility of the optimized cutter support plate and the standard deviation of the global failure coefficient meet the design requirements and working requirements of the cutter support plate of the shield machine, thereby verifying the effectiveness of the method.

[0138] The above embodiments are only used to illustrate the technical solutions of the present application, but not limit the same; although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the technical solutions recorded in the foregoing embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.​

Claims

1. An isogeometric robust topology optimization method for composite structures considering thermal coupling, characterized in that The method comprises the following steps: Step 1: constructing an isogeometric analysis model of the composite structure to obtain the density of control points; Step 2: based on the internal temperature uncertainty description of the composite structure, constructing a global thermal load considering internal temperature fluctuations according to the uncertainty description and the density of the control points, and generating the global flexibility of the composite structure; taking the density of the control points as a design variable, combining the uncertainty description, the global flexibility, the stress constraint and the optimization space utilization constraint, constructing an isogeometric robust topology optimization model of the composite structure considering thermal-mechanical coupling, and minimizing the mean value and standard deviation of the thermal flexibility of the composite structure under the influence of the internal temperature uncertainty of the composite structure under the constraint condition; Step 3: calculating the global stiffness matrix of the composite structure considering the bimodulus characteristics; Step 4: calculating the thermal strain of the composite structure at the Gauss point of the unit, combining the elastic tensor matrix considering the bimodulus characteristics, solving the global thermal load of the composite structure considering the internal temperature fluctuations, and solving the global displacement under the influence of the internal temperature uncertainty of the structure through the global thermal load of the structure and the global stiffness matrix of the structure, which is used to determine the global flexibility; solving the global failure coefficient of the composite structure considering the internal temperature fluctuations, which is used for the stress constraint; Step 5: constructing an objective function based on the mean value and standard deviation of the thermal flexibility of the composite structure and solving it to obtain the worst objective performance function; Step 6: calculating the worst limit state corresponding to the stress constraint; Step 7: updating the control point density according to the sensitivity of the worst objective performance function, the worst limit state and the optimization space utilization constraint with respect to the density of the control points to obtain the optimal design variable.

2. The method of isogeometric robust topology optimization of composite structures considering thermal coupling according to claim 1, characterized in that: The step 2 comprises the following steps: Step 2.1: Describing the internal temperature of the composite structure affected by multi-source uncertainty as a probability variable satisfying an inexact normal distribution T I represents the internal temperature variable of the composite structure, I μ and I σ respectively represent the mean and standard deviation of the internal temperature variable of the composite structure with interval characteristics, specifically: wherein, and respectively represent upper and lower limit values corresponding to the mean value and standard deviation of the temperature variable inside the composite structure. Step 2.2: Construct the overall thermal load F considering the thermal expansion phenomenon of the composite material under high temperature scenarios, considering internal temperature fluctuations th (ρ, T I ), ρ represents the control point density vector; Step 2.3: constructing an isogeometric robust topology optimization model of the composite structure considering thermal-mechanical coupling based on the non-precise probability variable and the global thermal load: s.t. g V (p) = V(p) / V0≤ [V] K B (p) U = F m + F th (p, T I ) p = {p i,j}, 10 -9 ≤ p i,j ≤ 1 i = 1,2,..., m; j = 1,2,..., n Where, ρ i,j Indicates control point P i,j The corresponding density, and c(ρ,T) represents the mean and standard deviation of the thermal flexibility of the composite structure considering the influence of internal temperature uncertainty. I ) represents the thermal flexibility of the composite material structure under the influence of internal temperature uncertainty, u e (ρ,T I () represents the displacement vector of element e under the influence of temperature uncertainty within the composite material structure, hereinafter abbreviated as N represents the stiffness matrix of element e considering bimodal characteristics. e G represents the number of units e. V (ρ) represents the optimization space utilization constraint function, V(ρ) represents the current optimization space size, V0 and [V] represent the design domain size and the upper limit of the space utilization constraint, respectively, and P(·) represents the probability calculation function. and [ω] TW ] represents the global failure coefficient constraint performance function of the composite material structure constructed based on the failure criterion, and the set upper limit value of the global failure coefficient, respectively. t K represents the pre-defined stress constraint reliability requirement. B (ρ) represents the overall stiffness matrix of the composite structure considering bimodal characteristics, U represents the overall displacement amplitude vector of the composite structure, and F m μ represents the external load on a composite material structure. T σ represents the mean value of the internal temperature variable of the structure. T This represents the standard deviation of the temperature variable inside the structure.

3. The method of isogemetric robust topology optimization of a composite structure considering thermal coupling of claim 1, wherein: The step 3 comprises the following steps: Step 3.1: obtaining the elastic tensor matrix considering the bimodulus characteristics, and solving the element stiffness matrix of the composite structure considering the bimodulus characteristics; Step 3.2: calculating the global stiffness matrix of the composite structure through the element stiffness matrix.

4. The method of isogemetric robust topology optimization of a composite structure considering thermal coupling of claim 1, wherein: The isogeometric analysis model in the step 1 is a non-uniform rational B-spline grid model, and the whole grid model is subjected to Gauss subdivision, so that the corresponding control points of the element e are used to obtain the element Gauss points in the i-th row and j-th column in the e-th element density 5. The method of isogeometric robust topology optimization of composite structures considering thermal coupling according to claim 4, characterized in that: The step 4 comprises the following steps: Step 4.1: Calculate unit Gaussian points thermal strain of the composite structure, in particular: wherein, denotes the structural thermal strain vector at a unit Gaussian point, Φ c denotes the composite thermal expansion coefficient vector, T R denotes the reference ambient temperature; T I denotes the temperature variable inside the composite structure; Combined with the Gauss subdivision method, the thermal load corresponding to the e th element is solved, and the specific calculation is as follows: wherein, represents the thermal load vector at element e, N G represents the number of discrete Gauss integration points in the row and column directions within each element of the parametric domain, represents the weights corresponding to the discrete Gauss integration points in the row and column directions within each element of the parametric domain, represents the strain-displacement matrix at element Gauss point J e represents the Jacobian matrix of element e, det( ) represents the operation of solving the determinant, represents the elastic tensor matrix considering the bimodular behavior; Step 4.2: Obtain the overall thermal load F of the composite structure by combining the thermal load vectors at the element e th (ρ, T I ); Step 4.3: Solve the stress vector at the Gauss point of the composite structure element considering internal temperature fluctuations, specifically: ​ wherein, denotes the unit-Gaussian point stress vector considering internal temperature fluctuations, hereinafter abbreviated as Step 4.4: Calculate the global failure coefficient of the composite structure based on the failure criterion and the cohesion function Specifically: where N e represents the number of isogeometric elements, represents the failure coefficient at the Gauss point of the element, p obtained by Tsai-Wu failure criterion and the stress vector of the Gauss point of the element t represents the P-mean condensation function coefficient of the stress constraint function.

6. The method of isogemetric robust topology optimization of a composite structure considering thermal coupling of claim 1, wherein: The step 5 comprises the following steps: Step 5.1: Introducing the weight coefficient w T , defining the weighted objective function wherein, and respectively represent the mean and standard deviation of the thermal compliance of the composite structure considering the influence of the internal temperature uncertainty, c(ρ, T I ) represents the thermal compliance of the composite structure under the influence of the internal temperature uncertainty, ρ represents the density of the control points, T I represents the internal temperature variable of the composite structure; Step 5.2: Calculate the approximate value of the thermal compliance c(p, T I ) of the composite structure with origin at E[c m (p, T I )] and compute the mean and standard deviation of the thermal compliance of the structure under the influence of the internal temperature uncertainty T I by the approximate value; Step 5.3: Rewrite the objective function as: wherein, represents the hth Gauss-Hermite integration point corresponding internal temperature value of the structure; represents the hth Gauss-Hermite integration point corresponding internal temperature of the structure thermal compliance of the structure under h represents the weight corresponding to the hth integration point, where h = 1, 2, …, H; Step 5.4: Solve the objective function considering the interval characteristics of the internal temperature variable distribution parameters Regarding the internal temperature mean I μ The sensitivity of the standard deviation I σ The worst objective function value corresponding to the internal temperature distribution parameter value of the structure is obtained based on the gradient search algorithm and The worst temperature condition And the worst objective performance function 7. The method of isogemetric robust topology optimization of a composite structure taking thermal coupling into account according to claim 6, characterized in that: Step 5.2 specifically comprises the following steps: Step 5.2.1: Considering the probabilistic distribution characteristics of the internal temperature variable, the internal temperature variable T of the structure is converted into a standard normal variable T by standardization processing, specifically: I T = (T - T ) / s s where T is the mean value of the internal temperature variable T, and s is the standard deviation of the internal temperature variable T. Step 5.2.2: calculating the origin matrix approximation value when m=1,2 based on Gauss-Hermite integration, specifically: where c(ρ, T I ) and c s (ρ, T s ) represent the structural thermal compliances represented by the structure internal temperature variable T I and the standard normal variable T s , respectively, ρ represents the density of the control point, φ(T s ) represents the probability density distribution function of the standard normal variable T s , H represents the number of selected integral points, w h represents the weight corresponding to the hth integral point, where h = 1, 2,..., H; is the standard normal variable value corresponding to the hth integral point, represents the structural thermal compliance represented by ; Step 5.2.3: Calculate the structural internal temperature uncertainty T I The mean and standard deviation of the structural thermal compliance under the influence of the temperature uncertainty T, in particular:

8. The method of isogemetric robust topology optimization of a composite structure considering thermal coupling of claim 1, wherein: The step 6 comprises the following steps: Step 6.1 : Stress-based performance function The limit state function is constructed and is expressed as: wherein, and [ω TW ] respectively represent a global failure coefficient constraint performance function of the composite structure constructed based on a failure criterion and a set upper limit value of the global failure coefficient, ρ represents the density of the control point, T I represents an internal temperature variable of the composite structure; Step 6.2: Consider the structure internal temperature variable T in the original space I Satisfy the non-precise normal distribution, the variable T in the original space I Transform the variable T in the original space to the standard normal space by standardization s Rewrite the limit state function as a function of the standard normal variable T s And the interval variable I μ And I σ The form represented by Step 6.3: establishing a reliability model for solving the worst limit state function on the reliability index surface under the influence of the non-precise probability variable: s.t.||T s ||=β t Where, β t This represents the reliability index corresponding to the constraint performance function, and is derived from its corresponding reliability requirement P. t Calculations show that β t =Φ -1 (P t );Φ -1 (·) denotes the inverse function of the standard normal cumulative distribution function, ||·|| denotes the operation of finding the modulus, μ T σ represents the mean value of the internal temperature variable of the structure. T This represents the standard deviation of the temperature variable inside the structure. and These represent the upper and lower limits of the mean and standard deviation of the temperature variable inside the composite material structure, respectively. Step 6.4: Calculate the stress limit state function Regarding variable T s , I μ and sensitivity of I σ ; through the gradient search algorithm, the worst constraint performance point on the reliability index surface is calculated and the worst limit temperature mean value and standard deviation are combined to obtain the worst limit temperature and the worst limit state function 9. The method of isogemetric robust topology optimization of a composite structure considering thermal coupling of claim 1, wherein: In the step 7, the sensitivity of the worst objective performance function, the worst limit state function and the optimization space utilization constraint with respect to the density of each unit control point is calculated; according to the control point density sensitivity calculation result, the control point density is updated combined with the moving asymptote method, and the convergence condition is checked, that is, the average value of the relative change degree of the worst objective performance function in a plurality of continuous iteration steps is not higher than a threshold value, if the convergence condition is not satisfied, the step 3 is returned for iteration.

10. An isogeometric robust topology optimization system for composite structures considering thermal coupling, characterized in that The method of isogeometric robust topology optimization of composite structures considering thermal coupling according to any one of claims 1 to 9, wherein the topology optimization is performed to obtain an optimal composite structure design variable.

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